The thermal expansion of an edge-restrained plate results in a "humping" of the plate. If the plate is being used as a reference plane for sensitive equipment, the thermal deformation will be felt by the equipment as an undesirable rotation of the reference plane. In some applications, an angular error as small as one mrad can be of significance. For example, where the plate is a roof of a tank turret and a gun sight is mounted on the roof, a one mrad deflection of the sight can represent, for a target 4 km away, an increase of over 4 meters in the impact point of a shell. This will very seriously degrade the sighting accuracy of the gun.
While thermal deformation can be measured directly using mechanical or optical techniques, the mechanisms available are practical only in a laboratory environment and are unsuited for use in a difficult or extreme environmental conditions.
Experimental studies have now shown that with a radiantly heated edge restrained plate, the flow of heat from the center of the plate to the restraining edges produces a significant temperature gradient in the edge area. It has also been found that the angular deflection of the plate at a given point is a linear function of this temperature gradient. Thus, the angle of rotation at any given point on the plate can be determined from the equation: EQU .theta.=K1.DELTA.T (1)
Where
.theta. is the angle of plate rotation at the location in question; PA1 .DELTA.T is the temperature differential between two reference points on the plate; and PA1 K1 is a constant with a value dependent on the location of interest on the plate and the positions where the temperatures are measured. PA1 .theta.is the angle of plate rotation at the location in question; PA1 T is the measured plate temperature at a given point; PA1 T INITIAL is the initial temperature of the plate at the point where T is measured; and PA1 K2 is an experimentally or analytically determined constant.
The constant K1 may be determined either experimentally or using an analytical model of the edge restrained plate.
Further analytical studies has shown that with an edge-restrained plate that is convectively cooled, the rotation of the plate from an initial state is a linear function of the difference between the actual plate temperature and an initial temperature at the initial state. Thus, the angle of rotation at any given point on the plate can be determined using the equation: EQU .theta.=K2(TT-T INITIAL) (2)
Where
The above equations can be used to monitor changes in the orientation of an instrument due to thermal deformation of an edge-restrained plate on which the instrument is mounted. Once the orientation changes are known, compensating corrections can be made.